A New Convexity Measure Based on a Probabilistic Interpretation of Images

In this article we present a novel convexity measure for object shape analysis. The proposed method is based on the idea of generating pairs of points from a set, and measuring the probability that a point dividing the corresponding line segments belongs to the same set. The measure is directly applicable to image functions representing shapes, and also to gray-scale images which approximate image binarizations. The approach introduced gives rise to a variety of convexity measures, which makes it possible to obtain more information about the object shape. The proposed measure turns out to be easy to implement using the Fast Fourier Transform and we will consider this in detail. Finally, we illustrate the behavior of our measure in different situations and compare it to other similar ones.

• Type: Journal
• Year: 2006
• Where: PAMI
• Authors: Esa Rahtu, Mikko Salo, Janne Heikkilä
• Keywords: Convexity Measures, Corresponding Line Segments, Image, PAMI 2006